The United States Tax Court recently decided that payments for sex-reassignment surgery are deductible as medical expenses. Among the 15 judges, there were six separate opinions, with five of the judges dissenting. Most of the debate dealt with questions like whether Gender Identity Disorder is a “disease” (a key term in the statue) and if so whether sex-reassignment surgery, which doesn’t change the patient’s subjective sense of gender identity, constitutes a “treatment” for the disease (ditto).

Those are issues with interesting linguistic dimensions, but what I want to talk about here is a different aspect of the case: the dispute about how to interpret disjunction under negation—i.e., how to interpret expressions such as I don’t know anything about linguistics or tax law (with don’t signaling negation and or signaling disjunction).

In the case decided by the Tax Court, the IRS had ruled that sex-reassignment surgery isn’t deductible, on the theory that it amounts to cosmetic surgery, which the tax code excludes from its definition of medical care. The code defines cosmetic surgery as—

any procedure which is directed at improving the patient’s appearance and does not meaningfully promote the proper function of the body or prevent or treat illness or disease.

The language in boldface is what’s at issue here.

The Tax Court rejected the IRS’s position, with the majority of the judges concluding that sex-reassignment surgery was a treatment for the disease of Gender Identity Disorder and therefore wasn’t cosmetic surgery. (The majority didn’t decide the question whether the procedure is “directed at improving appearance”—though that’s how the dissenters characterized it—or whether it promotes the proper function of the body.)

On the majority’s interpretation, the boldfaced language above means that an appearance-improving procedure doesn’t count as cosmetic surgery if it either promotes proper bodily function or prevents or treats illness or disease. The dissenters, on the other hand, argued that for such a procedure to be excluded from the cosmetic-surgery category, it has to both promote proper bodily function and prevent or treat illness or disease. In other words, the dissenters were equating (1a) with (1b), while the majority equated it with (1c):

1a. does not [(meaningfully promote…) or (prevent or treat…)]

1b. [does not meaningfully promote…] or [does not prevent or treat]

1c. [does not meaningfully promote…] and [does not prevent or treat]

One of the dissenting opinions accused the majority of ignoring the statute’s plain meaning:

The majority's analysis proceeds as if the statute employs “and” rather than “or” between the “meaningfully promote the proper function of the body” and “prevent or treat illness or disease” prongs. Respondent appears to agree with this interpretation in lieu of a plain reading of the statute. In essence, the majority and respondent engage in reconstruction, rather than strict construction, of section 213(d)(9).

Judge Halpern, who voted with the majority and wrote a separate concurring opinion, wasn’t buying this argument. In explaining why he didn’t buy it, he invoked principles of formal logic:

Because the second part of the test contains two expressions separated by “or”, that part of the test contains a “disjunction”; i.e., a compound proposition that is true if one of its elements is true. Importantly, however, the second part of the test contains not just a disjunction (i.e., (p or q)), but rather the negation of a disjunction (i.e., not (p or q)). Judge Foley errs because he assumes that the expression “not (p or q)” is equivalent to the expression “(not p) or (not q)”….

In formal logic, there is a set of rules, De Morgan's laws, relating the logical operators “and” and “or” in terms of each other via negation. [Citation to Wikipedia.] The rules are:

not (p or q) = (not p) and (not q)

not (p and q) = (not p) or (not q)

The first of the rules would appear to govern the disjunction in section 213(d)(9)(B), which is of the form “not (p or q)”.

To which the dissenters responded:

Judge Halpern’s mechanical application of De Morgan’s laws is not prudent. Simply put, congressional intent is not subservient to De Morgan’s laws.

Judge Halpern is right about what the statute’s language means, but in framing his explanation in terms of formal logic, he’s on somewhat shaky ground (and not just because he opened himself up to the dissent’s glib putdown). The problem is that natural languages don’t necessarily follow the rules of formal logic. Indeed, the whole point of formal logic is to provide an artificial language that avoids the messiness of natural language.

Now, it just so happens that for expressions in the form not (p or q), English does in fact behave consistently with De Morgan’s law. Or at least it usually does. The sentence I’m not free this week or next week is generally interpreted to mean ‘I’m not free this week and I’m not free next week.’ But it can also be interpreted to mean ‘Either this week or next week—I can’t remember which one—I’m not free.’ (These examples are adapted from the Cambridge Grammar of English Language.) I suspect that the latter interpretation arises only in a fairly narrow range of contexts, but in any event, the point remains that De Morgan’s laws don’t invariably apply in English.

There’s an even bigger deviation from De Morgan’s laws in the case of negated conjunction (as opposed to negated disjunction). According to De Morgan’s laws, not (p and q) = (not p) or (not q). But in English, not (p and q) is more often interpreted as (not p) and (not q). So I’m not free this week and next week is generally interpreted as ‘I’m not free this week and I’m not free next week.’ But again the Morganian interpretation is also possible, especially (only?) if the and is stressed: I’m not free this week AND next week will typically be interpreted to mean ‘It is not the case that I’m free both weeks (but I am free one of them).’

Note that in the case of disjunction, stressing the coordinator (or) doesn’t have the same effect as in the case of conjunction. That is, it doesn’t cancel the default (non-Morganian) interpretation. On the contrary, it reinforces it. I’m not free this week OR next week is interpreted as ‘I’m not free this week AND I’m not free next week.’

Not all languages follow the same pattern as English. For instance, Japanese apparently doesn’t follow De Morgan’s laws in the case of negated disjunction. So in Japanese, not (p or q) = (not p) or (not q). Or at least that’s true for adult speakers of Japanese. Young Japanese-speaking children, it seems, do follow De Morgan’s laws, but then switch over when they more completely master the language. (See, for example, Andrea Gualmini & Stephen Crain, "Why No Child or Adult Must Learn De Morgan's Laws", Proceedings of the 24th Annual Boston University Conference on Language Development, Cascadilla Press, Somerville, MA (2004).)

In fact, Stephen Crain argues that in all languages disjunction is interpreted consistently with De Morgan’s law in at least some structures, and that this is evidence supporting the nativist side of the debate over whether knowledge of language is innate. Here’s the abstract to his paper "The Interpretation of Disjunction in Universal Grammar":

Child and adult speakers of English have different ideas of what ‘or’ means in ordinary statements of the form ‘A or B’. Even more far-reaching differences between children and adults are found in other languages. This tells us that young children do not learn what ‘or’ means by watching how adults use ‘or’. An alternative is to suppose that children draw upon a priori knowledge of the meaning of ‘or’. This conclusion is reinforced by the observation that all languages adopt the same meaning of ‘or’ in certain structures. For example, statements of the form ‘not S[A or B]’ have the same meanings in all languages, and disjunctive statements receive a uniform interpretation in sentences that contain certain focus expressions, such as English ‘only’. These observations are relevant for the long-standing “nature versus nurture” controversy. A linguistic property that (a) emerges in child language without decisive evidence from experience, and (b) is common to all human languages, is a likely candidate for innate specification. Experience matters, of course. As child speakers grow up, they eventually learn to use ‘or’ in the same way as adults do. But, based on findings from child language and cross-linguistic research, it looks like certain aspects of language, including the interpretation of disjunction, are part of the human genome.

There are some obvious questions: Is Crain correct in saying that disjunction is interpreted consistently with classical logic in (at least some constructions in) all languages? And that adult speech in languages like Japanese really provides children learning to speak no evidence for the interpretation of disjunction that they start out with?

However, I’m pointing out Crain’s work, not as an opening to talk about whether there’s such a thing as Universal Grammar, but as an exercise in Six Degrees of Something-or-Other. Here we have a decision interpreting the United States Internal Revenue Code that turns (at least in part) on an issue that might be relevant to figuring out the fundamental nature of language. And I thought tax law was boring.

39 Comments

I am trying to think of some other procedure that could be potentially said to either "meaningfully promote the proper function of the body" or "prevent or treat illness or disease," but not both. Perhaps electroconvulsive therapy? ECT does not particularly help the body's proper functions — quite the opposite, in fact — but can be effective in treating some kinds of persistent depression. Or, I suppose, once could include any number of psychopharmaceuticals whose positive effects are all in the realm of the mind but whose negative side-effects are physical. I assume that such treatments are tax-deductable.

Well it's easy to think of things that promote the proper function of the body but do not treat an illness or disease. For instance consider setting a broken bone. I suspect infertility treatments also get covered under this disjunct.

As far as something that treats illness or disease but doesn't meaningfully promote the proper function of the body consider treatment to treat a passive carrier of some bacterial/viral illness. Their body function may not be meaningfully affected at all by the presence of the bacteria/virus but you are still treating a disease when you eliminate the bacteria/virus from their system.

Alternatively one might count the treatments to sever the nerves in the spinal column to alleviate the horrific pain caused by some kinds of cancers as treating (the symptoms) of a disease/illness while actually disrupting the proper functioning of the body.

There are often statute-interpretation statutes which permit or to be replaced with and and vice versa, singulars to be replaced with plurals and vice versa, masculine pronouns to be …. You get the idea.

Richard said,

For I'm not free this week and next week to sound morganic, I don't think stressing the and is necessary or sufficient. I could hear it as immorganic with a certain kind of stress, while if you pause, making the last three words sound like an afterthought, it sounds morganic without stress.

Barbara Partee said,

Really nice post! I agree with everything you said. But I don't know the answers to your questions at the end.

Note about non-de-Morgan languages. Russian is at least superficially another non-de-Morgan language for adults; the Russian 'ili' ('or') is a "Positive Polarity Item" — i.e. it doesn't want to be under negation. So when you get "not p or q", it really can't be interpreted as not (p or q), because that 'or' can't occur under negation. Therefore you only get the reading where the 'or' is higher — "not p or not q (I don't remember which)". (This might be a metalinguistic 'or' — marking a disjunction between two speech acts. "I'm saying this or I'm saying that, I don't know which." I think one could argue that statutes would never be using that one — it would be as if the framers of the law hadn't decided which version of the law they wanted to adopt.

By the way, Russian doesn't suffer from that behavior of 'ili', because it has a different form 'ni' ("nor") which is used for 'not (p or q)', which is obligatorily expressed, in effect, as 'not p nor q'.

J. Goard said,

Huh? Wouldn't the stressed and serve to make it immorganic? I think you switched the terms there.

Anyway, this example doesn't neccessarily go against De Morgan's on the (for me) primary reading where I'm not free this week and I'm not free next week, because in that case it could very well be that not free is interpreted as a constituent. (Similar to I'm busy this week and next week.) i.e., you don't have to do the immorganic rule NOT(free this week AND free next week) ==> NOT(free this week) AND NOT (free next week), because you never have the first part, but instead have (NOT free)(this week AND next week), and then the (NOT free) distributes exactly like (busy) would.

This becomes crystal clear if we explicitly distribute (free): I'm not free this week and free next week. To my mind, the negation must distribute morganically.

Does this mean the dissenters have an alternate set of logical substitutions which they claim works consistently for the legal language being analysed; or are they claiming that all these ands, ors and nots are largely uninterpretable if you don't already understand the intent of the law?

Rubrick said,

This notion of trying to decide on the "plain meaning" of a sentence via argument has always struck me as ridiculous. It seems to me that there is one and only one way to determine the truth of the matter: get a suitably large and representative sample of native speakers and ask them what they think the sentence means. If the vast majority of respondents interpret it the same way, it's decided. Case closed. If there's a fairly even split among alternatives, then there is no "plain meaning". Then the courts can resort to argument.

As for "congressional intent", if this is deemed important, ask them. This business of arguing what they must obviously have meant is silly if they're still alive and able to answer for themselves.

jo said,

About the case of Japanese, the Gualmini & Crain (2002) article linked to above does not (on a quick skim-read) really give any details. If, like me, anyone was wondering what kind of sentences are used to test the interpretation of not (p or q) in Japanese, some examples are given in the abstract for a 2008 paper by Theres Gruter, Moti Lieberman and Andrea Gualmini here: http://www.mcgill.ca/files/linguistics/AcquiringtheScopeofDisjunction.pdf

We discussed a similar situation a couple of years back: see Exclusive OR: free dinner and stay out of jail. I agree with you that the fairest test is to ask whether it's idiomatic, but the whole dispute seems to lie in legal thinking, which tends to treat language as a logical construct.

The idiomatic meaning here seems to me so clearly what the majority said (i.e. if it does either of the things on the list, it isn't cosmetic surgery) that I can't tell if the IRS really believed otherwise or were just trying the argument on because it suited their position (presumably maximising what is taxable).

Mr Punch said,

This is "special pleading" on the part of the dissenting judges, I believe. There are many, many legal tests (in, e.g., employment law) that are structured similarly, and as far as I know "or" is always interpreted as "and/or" not "either … or" in such cases.

Bryan said,

JT said,

I agree with J. Goard; Particularly, De Morgan's laws apply to propositions; (not (or P Q)) is equivalent to (and (not P) (not Q)) where P and Q are propositions. In most (all?) of the examples, there are some options about what to takes as P and Q. When P and Q are clear, do De Morgan's laws hold consistently? E.g., (Assuming a way to get the `bracketing' understood correctly, does the meaning of "It is not the case that [[I am free this week] and [I am free next week]]" change if the "and" is stressed? What about the "or" in "It is not the case that [either [I am free this week] or [I am free next week]]"? It'd be interesting to see examples where De Morgan's laws don't apply, but in which P and Q are unambiguous. Or perhaps rather than "De Morgan's laws don't apply in language X" the claim should be, e.g., "in language X, `not P or Q' expresses the proposition (or (not P) (not Q)), rather than (not (or P Q))".

T-Rex said,

Edward M. "Ted" McClure said,

From the discussion above and the extensive dissent, we have a clear indication that this statute is ambiguous. Mr. Goldfarb's statement says as much: "Now, it just so happens that for expressions in the form not (p or q), English does in fact behave consistently with De Morgan’s law. Or at least it usually does. The sentence I’m not free this week or next week is generally interpreted to mean ‘I’m not free this week and I’m not free next week.’ But it can also be interpreted to mean ‘Either this week or next week—I can’t remember which one—I’m not free.’" The next step in construction, therefore, is examination of the legislative history to ascertain the intent of Congress.

AlexTheSeal said,

The problem is that natural languages don’t necessarily follow the rules of formal logic. Indeed, the whole point of formal logic is to provide an artificial language that avoids the messiness of natural language.

Well, almost. Formal logic in its infant form as developed by the ancients and by the Scholastics was intended to codify certain forms of argument, if you will, that already existed in natural language. Natural language doesn't follow (or not follow) deMorgan's laws; rather, deMorgan's laws follow (or, more precisely, describe in an idealized way) natural language. Somewhere along the line the cart got put before the horse, and people got the Platonic idea that formal logic was prior to natural language, the latter a pale shadow of the former. That confusion is at the heart of many "but the language as used doesn't make any logical sense!" battles.

Boris said,

If children are born with an innate understanding of what "or" means, how can it possibly mean something else to adults? Did some adult say once upon a time "let's change the meaning of or" or do adults "forget" this innate knowledge and have to reinvent it? I find that unlikely. It must mean that whatever innate understanding of logic exists must be so inadequate as to be completely lost in adulthood.

Guest14 said,

Army1987 said,

The dissenters' interpretation treats the two "or" differently; if they were consistent in their interpretation, they'd have to say that non-cosmetic surgery would have to promote the proper function of the body, AND to prevent AND treat illness AND disease. *shrug* (I'm not denying that there can be sentences in which "or" is used twice with two different meanings, but this one definitely *doesn't* sound like one of them.)

(The idealistic side of me *defines* "illness" and "disease" as "failure of the body to properly function", so according to it the whole discussion is moot. It considers the brain to be part of the body, so that ECT and psychofarmaceuticals would be covered; it consider ability to reproduce to be part of the proper body function, so that infertility treatments would be covered; but it doesn't consider asymptomatic infections as illnesses. Anyway, it refuses to tell whether or not the gender identity disorder is a disease. Too bad no lawyer would agree with it…)

Sandra said,

2 comments:
1. I was at a conference several years ago where a Queer Studies speaker objected to the inclusion of Gender Identity Disorder in DSM because he thought that it's mere inclusion meant it's a disease or mental illness and was therefore anti-gay. I said it was positive because it established diagnostic criteria for possible surgery. It's common with the DSM for people to think that if you have any condition listed there it means you're crazy.
2. I had a facelift covered by my health insurance some years ago. I had had a lot of jaw surgery and my face still didn't look right (mainly because of the condition that led to the surgery). The doctor made a case to my insurance that it was part of the entire treatment of the condition, even though this part was purely cosmetic. So even insurance companies can sometimes be flexible in how they interpret their own language.

cosmetic surgery … (does not meaningfully promote the proper function of the body) or (prevent or treat illness or disease)

As a programmer, I think along the mathematical lines and see:

if ((not promoting function) and (not prevent/treat disease))

which follows, conveniently, De Morgan's laws. Perhaps the panel should have considered the argument in Being Logical, by McInerny on 'Negative Statements'.

Interestingly enough, thinking like a programmer confuses things at home as well. I break down sentences like this one and parse each part. When I repeat it back to the wife, she says 'no, that is not what I am saying'. So, while the dissenting opinion is a little self-righteous, as perhaps was the prevailing opinion; the truth remains that even while the explanation might be faulty, it appears to be valid reasoning.

Ran Ari-Gur said,

@Boris: Yeah, I'd be interested to see those studies. I wonder if maybe it's just that children often follow De Morgan's laws rather than their languages' rules. Like how (to choose a classic example) English-speakers without native /h/, when trying to imitate /h/-ful dialects, will put a lot of /h/'s where they don't belong, and still miss lots of /h/'s that do; to a speaker who has /h/ natively, it sounds like such speakers are getting it 100% wrong, putting /h/'s in exactly the wrong places, but what's really happening is, they only notice the errors. So if those studies worked by actively testing children's applications of negated conjunction and disjunction, or by examining a large corpus of children's speech, then those conclusions seem very surprising to me (as to you), but if they're simply observing that this is a thing that happens, then it's less surprising. (Their argument seems the same whether or not this is something that all children always do, since their point is just that it happens whether or not the language is one where it's right.)

SSP said,

The dissenting opinion wasn't valid reasoning. The policy was C = not (f or t) [cosmetic = not (for function or for treatment)]. Therefore, C = (not f) and (not t) is true — lip surgery is cosmetic because it is both not for function and not for treatment. But the dissenters conflated C with (not C). "The dissenters, on the other hand, argued that for such a procedure to be excluded from the cosmetic-surgery category, it has to both promote proper bodily function and prevent or treat illness or disease." This is saying: (not C) = (f and t). This is wrong. C = not (f or t), so (not C) = not (not (f or t) ) = (f or t). So, something is not cosmetic if it is either for function or for treatment.

I think the post makes a good point about language not always following rules of formal logic. But I think that in this case, the language does fit with formal logic. As an English speaker, when I read "cosmetic surgery does not promote function or provide treatment," I think that something is not cosmetic surgery if it either goes to function or to treatment. I think most English speaker probably think the same thing, although I haven't conducted a study. And I think this is the same conclusion that De Morgan' principle shows.

jfruh is asking the right question from a statutory iterpretation perspective, and Peter Gerdes is providing the right answer to the question from the same perspective. Content often sheds light on otherwise ambiguous grammar, and the tax code contains far more ambiguous grammar than it should (in part because key provisions are often drafted in a hurry during last minute deal making).

The sensible place to start in statutory interpretion is to look at each possible reading and see which one makes sense.

Requiring non-cosmetic surgery to both "meaningfully promote the proper function of the body" and also to "prevent or treat illness or disease," excludes hospice treatment (which isn't design to make you function right) and also excludes trauma care (which isn't an illness or disease). Requiring that a treatment "meaningfully promote the proper function of the body" and also "prevent or treat illness or disease" over overlaps, but the cases when they don't argue for the broader definition. And, if there was exact overlap, there wouldn't be any reason to include both phrases, so they must mean something different.

I do think you could make that both prongs are met in gender reassignment surgery. DSM-IV does classify the condition as a disease. Gender reassignment surgery treats that disease. Many treatments don't "cure" the disease (a judge apparently thinks that only a change in subjective gender identity would be a cure) they simply make the symptoms more bearable (pain killers, for example). Also, aligning gender identity more closely with bodily appearance promotes the idea that body and mind ought to be in harmony, if you can't change one, change the other.

Improving appearance alone, of course, is a product of all sorts of medical treatment. Cleft lips, boils, and untreated broken legs all look damn ugly.

The other context specific issue that does go to the heart of the merits is that the reason cosmetic surgery is not tax deductible is because of the belief that we don't want to have tax incentives to purchase a luxury. One way to think about that issue is whether tax treatment is likely to impact demand much. In the case of cosmetic surgery, the impact is likely to be real. There is a big "soft" market for cosmetic surgery that varies with cost and fund availability. In the case of gender reassignment, not so much. Middle class folks across the nation are not going to surge in huge numbers to gender reassignment centers like Trinidad, Colorado because they now they that the bill is tax deductible.

I'm surprised no one's mentioned chemotherapy as failing the "and" interpretation of that statute: it treats an illness but is quite detrimental to the proper function of the body. I'm sure insurance companies have found all sorts of reasons to deny coverage for it, but I really doubt that any of them have done so on the grounds that it's a cosmetic procedure, not least because it leaves people looking absolutely awful.

If the statute specifically covers surgical procedures, a more pertinent example would be amputation. A friend of mine was in terrible pain from foot problems that were essentially unfixable. She eventually elected to have her foot amputated, and is now much happier. Her foot was not diseased, and it could be argued that cutting off a "healthy" appendage was detrimental to the proper function of her body; but it was also absolutely the right thing to do for her health and well-being.

The brain and the body are really not as separate as people seem to think; it's quite reasonable for some mental health problems to be treatable through surgery, just like others might be treated with medications or massage or other physical remedies. I'm very glad the judges decided the way they did.

[…] Into Force Sex Reassignment Surgery and De Morgan's Laws February 21, 2010 Via "Sex-change surgery and universal grammar", a post on a decision of the Tax Court earlier this month. The decision addressed the question of […]